Question: $A$ $B$ $C$ If: $ BC = 4x + 2$, $ AB = 8x + 8$, and $ AC = 22$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {8x + 8} + {4x + 2} = {22}$ Combine like terms: $ 12x + 10 = {22}$ Subtract $10$ from both sides: $ 12x = 12$ Divide both sides by $12$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $BC$ $ BC = 4({1}) + 2$ Simplify: $ {BC = 4 + 2}$ Simplify to find ${BC}$ : $ {BC = 6}$